add numerical recipes library

lib/nr/cpp/recipes/qrdcmp.cpp

@@ -0,0 +1,34 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+void NR::qrdcmp(Mat_IO_DP &a, Vec_O_DP &c, Vec_O_DP &d, bool &sing)
+{
+	int i,j,k;
+	DP scale,sigma,sum,tau;
+
+	int n=a.nrows();
+	sing=false;
+	for (k=0;k<n-1;k++) {
+		scale=0.0;
+		for (i=k;i<n;i++) scale=MAX(scale,fabs(a[i][k]));
+		if (scale == 0.0) {
+			sing=true;
+			c[k]=d[k]=0.0;
+		} else {
+			for (i=k;i<n;i++) a[i][k] /= scale;
+			for (sum=0.0,i=k;i<n;i++) sum += SQR(a[i][k]);
+			sigma=SIGN(sqrt(sum),a[k][k]);
+			a[k][k] += sigma;
+			c[k]=sigma*a[k][k];
+			d[k] = -scale*sigma;
+			for (j=k+1;j<n;j++) {
+				for (sum=0.0,i=k;i<n;i++) sum += a[i][k]*a[i][j];
+				tau=sum/c[k];
+				for (i=k;i<n;i++) a[i][j] -= tau*a[i][k];
+			}
+		}
+	}
+	d[n-1]=a[n-1][n-1];
+	if (d[n-1] == 0.0) sing=true;
+}